The maximal subsemigroups of the ideals on a monoid of partial injections

2024/03/11 by Apatsara Sareeto, Sareeto, Apatsara, Jörg Koppitz +1
Decision Sciences · Mathematics · #20M12 #20M18 #20M20 #F.4.1 #FOS: Mathematics #Fuzzy and Soft Set Theory #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2403.06957

openalex publication_date 2024/03/11 · openalex created_date 2024/03/13 · openalex updated_date 2026/07/28

Abstract

In the present paper, a submonoid of the well studied monoid POI_n of all order-preserving partial injections on an n-element chain is studied. The set IOF_n^par of all partial transformations in POI_n which are fence-preserving as well as parity-preserving form a submonoid of POI_n. We describe the Green's relations and ideals of IOF_n^par. For each ideal of IOF_n^par, we characterize the maximal subsemigroups. We will observe that there are three different types of maximal subsemigroups.

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